Question:
If a graph is drawn between the Fahrenheit reading of the temperature of a body along y-axis and twice its Celsius reading on x-axis, then the angle made by the graph with x-axis is
If a graph is drawn between the Fahrenheit reading of the temperature of a body along y-axis and twice its Celsius reading on x-axis, then the angle made by the graph with x-axis is
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For any straight line:
\[
\tan\theta=\text{slope}
\]
Find the slope first and then determine the angle.
Updated On: Jun 17, 2026
- $\tan^{-1}(0.9)$
- $\tan^{-1}(2)$
- $\tan^{-1}(1.8)$
- $\tan^{-1}(0.5)$
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The Correct Option is A
Solution and Explanation
Concept:
The relation between Celsius and Fahrenheit scales is
\[
F=\frac{9}{5}C+32
\]
The slope of the graph determines the angle made with the x-axis.
Step 1: Express the equation in terms of x and y.
Given \[ y=F \] and \[ x=2C \] Therefore, \[ C=\frac{x}{2} \] Substituting into Fahrenheit equation, \[ y=\frac{9}{5}\left(\frac{x}{2}\right)+32 \] \[ y=\frac{9}{10}x+32 \]
Step 2: Find the slope of the graph.
Comparing with \[ y=mx+c \] we obtain \[ m=\frac{9}{10}=0.9 \]
Step 3: Determine the angle with x-axis.
\[ \tan\theta=m \] \[ \tan\theta=0.9 \] Hence, \[ \theta=\tan^{-1}(0.9) \] \[ \boxed{\tan^{-1}(0.9)} \]
Step 1: Express the equation in terms of x and y.
Given \[ y=F \] and \[ x=2C \] Therefore, \[ C=\frac{x}{2} \] Substituting into Fahrenheit equation, \[ y=\frac{9}{5}\left(\frac{x}{2}\right)+32 \] \[ y=\frac{9}{10}x+32 \]
Step 2: Find the slope of the graph.
Comparing with \[ y=mx+c \] we obtain \[ m=\frac{9}{10}=0.9 \]
Step 3: Determine the angle with x-axis.
\[ \tan\theta=m \] \[ \tan\theta=0.9 \] Hence, \[ \theta=\tan^{-1}(0.9) \] \[ \boxed{\tan^{-1}(0.9)} \]
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